張宏鈞臺灣大學：電信工程學研究所許森明Hsu, Sen-MingSen-MingHsu2007-11-272018-07-052007-11-272018-07-052004http://ntur.lib.ntu.edu.tw//handle/246246/58655本論文以採用曲線式混合基底元素之全向量有限元素波束傳播法來分析光波導問題。利用波束傳播法本身的特性，我們克服數個採用特徵值解法來分析光波導模態時遭遇的困難點。 　　經由分析橢圓狀纖芯的光纖，我們發現利用波束傳播法來分析高階模態的過程比利用特徵值解法來分析更為直觀，因為利用特徵值解法，需要為該演算法提供一適當的等效折射率初始值才可使計算結果收斂至期望之模態。 　　另外，本論文藉由引進一廣義的完美匹配層作為邊界條件來吸收超出數值空間之電磁波，也可以成它a分析具有非對角化之相對介電係數及導磁係數材料張量的LiNbO3光波導。而對於材料張量為對角化形式的結構，我們可以利用虛軸波束傳播法來加速分析過程。 　　藉由分析兩種具有不同空氣洞排列方式的多孔光纖之能量散逸特性，我們展示本論文的有限元素虛軸波束傳播法可以應用於具能量散逸特性的光波導分析，而且當光波導結構及計算的未知數數目很大時，利用此方法來進行分析會比採用特徵值解法來分析更為適合。A full-vectorial finite element beam propagation method based on curvilinear hybrid edge/nodal elements is adopted in this thesis for studying optical waveguide problems. Several difficulties of the finite element method eigenmode solver based on the (modified) shift inverse power method are overcome in this work by taking advantages of the characteristics of the beam propagation method. By analyzing the elliptical-core fibers, we find that the procedure for finding higher order modes using the beam propagation method is straightforward, while that of the eigenmode solver based on the shift inverse power method converges to the desired mode only when the initial guess for the effective index of the desired mode is properly assigned. Incorporating the general closed-form perfectly matched layer into the beam propagation method as the boundary condition to absorb waves out of the computational window, the proton-exchanged LiNbO3 optical waveguides with non-diagonal permittivity and permeability tensors can still be analyzed. For the cases in which the tensors are in diagonal form, the imaginary-distance beam propagation method can be employed to speed up the analysis process. Through the calculation of the leakage properties of two kinds of photonic crystal fibers with different air hole arrangements, we demonstrate that the finite element imaginary-distance beam propagation method can analyze the leaky modes reliably and it is more suitable for the waveguides with large structures and large number of unknowns than the finite element method eigenmode solver based on the modified shift inverse power method.1 Introduction 1 1.1 Motivations....................................... 1 1.2 Chapter Outline................................... 4 2 Mathematical Formulations and Related Techniques 6 2.1 Basics of Finite Element Eigenmode Solver......... 6 2.2 General Closed-Form Perfectly Matched Layers...... 9 2.3 Finite Element Beam Propagation Method............ 13 2.4 Imaginary-Distance Beam Propagation Method........ 19 3 Numerical Results of Conventional Fibers 25 3.1 Overview.......................................... 25 3.2 Circular Waveguides............................... 26 3.3 Elliptical-Core Fibers............................ 29 3.4 Summary........................................... 31 4 Numerical Results of Anisotropic Waveguides 62 4.1 Overview.......................................... 62 4.2 Anisotropic Embedded-Channel LiNbO3 Integrated Optical Waveguides................................ 64 4.3 Proton-Exchanged LiNbO3 (PE-LN) Optical Waveguides 65 4.4 Summary........................................... 66 5 Numerical Results of Photonic Crystal Fibers 78 5.1 Overview.......................................... 78 5.2 Triangular Holey Fibers........................... 81 5.3 Honeycomb Fibers.................................. 83 5.4 Summary........................................... 86 6 Conclusion 10713189307 bytesapplication/pdfen-US有限元素法光波導波束傳播法optical waveguidebeam propagation methodfinite element methodthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/58655/1/ntu-93-R91942015-1.pdf